Details

sample317.0ms

Algorithm

intervals

Results

261.0ms

3416×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	90	61
1	389	58
2	2115	36
3	5001	36

prune14.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.3b

Counts

2 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
120×	`times-frac`
89×	`add-cube-cbrt` `*-un-lft-identity`
40×	`add-exp-log` `add-cbrt-cube`
39×	`swap-sqr` `associate-r` `associate-l`
26×	`pow1`
12×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
4×	`add-log-exp`
3×	`pow2` `frac-times` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 214

Calls

4 calls:

10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series76.0ms

Counts

4 → 10

Calls

4 calls:

23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
30.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify74.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	426	1780
1	2077	1524
2	5002	1377

prune1.0s

Filtered

224 candidates to 146 candidates (65.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	209	15	224
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	210	16	226

Merged error: 0.5b

Counts

226 → 16

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ (* 1.0 1.0) (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

989×	`add-exp-log`
538×	`prod-exp`
477×	`add-cbrt-cube`
345×	`div-exp`
250×	`cbrt-unprod`
153×	`cbrt-undiv`
97×	`times-frac`
93×	`add-sqr-sqrt`
68×	`add-cube-cbrt` `*-un-lft-identity`
51×	`frac-times` `associate-*l/`
45×	`pow1`
39×	`associate-r`
32×	`pow-to-exp` `pow-exp`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
14×	`pow-plus` `pow-prod-up`
12×	`pow-prod-down`
9×	`div-inv`
8×	`pow3` `unpow2` `unswap-sqr`
4×	`add-log-exp`
3×	`sqrt-prod` `*-commutative`
2×	`pow2` `pow-sqr`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 400

Calls

4 calls:

31.0ms	(* (* (* (* (/ (* 1.0 1.0) (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series106.0ms

Counts

4 → 10

Calls

4 calls:

52.0ms	(* (* (* (* (/ (* 1.0 1.0) (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
31.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify92.0ms

Algorithm

egg-herbie

Counts

410 → 410

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	2065	6828
1	5002	4466

prune1.1s

Filtered

410 candidates to 140 candidates (34.1%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	398	12	410
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	408	18	426

Merged error: 0.2b

Counts

426 → 18

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ 1.0 (pow (fabs x) 6)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

131×	`add-sqr-sqrt`
120×	`times-frac`
82×	`add-cube-cbrt` `*-un-lft-identity`
52×	`add-exp-log`
51×	`associate-l`
40×	`add-cbrt-cube`
39×	`associate-r`
26×	`swap-sqr`
21×	`pow1`
18×	`div-exp`
16×	`prod-exp` `unswap-sqr`
12×	`cbrt-undiv` `cbrt-unprod`
11×	`unpow-prod-down`
10×	`div-inv`
5×	`sqr-pow`
4×	`add-log-exp`
3×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `sqrt-prod` `*-commutative`
2×	`pow2` `pow-to-exp` `pow-plus` `pow-exp` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 217

Calls

4 calls:

13.0ms	(* (/ 1.0 (pow (fabs x) 6)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series117.0ms

Counts

4 → 10

Calls

4 calls:

66.0ms	(* (/ 1.0 (pow (fabs x) 6)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
28.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify104.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	684	1784
1	3652	1546
2	5001	1414

prune1.1s

Filtered

227 candidates to 155 candidates (68.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	220	7	227
Fresh	12	5	17
Picked	1	0	1
Done	0	0	0
Total	233	12	245

Merged error: 0.1b

Counts

245 → 12

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b	(sqrt PI)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

333×	`add-exp-log` `add-cbrt-cube`
170×	`prod-exp` `cbrt-unprod`
125×	`pow1`
105×	`cbrt-undiv` `div-exp`
93×	`add-sqr-sqrt`
89×	`times-frac`
68×	`add-cube-cbrt` `*-un-lft-identity`
62×	`pow-plus` `pow-prod-up`
51×	`frac-times` `associate-*l/`
39×	`associate-r`
27×	`associate-l`
26×	`swap-sqr`
17×	`associate-*r/`
12×	`pow-prod-down`
10×	`pow2` `pow-sqr`
9×	`div-inv`
8×	`unswap-sqr`
4×	`pow3` `add-log-exp`
3×	`sqrt-prod` `*-commutative`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 332

Calls

4 calls:

27.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
10.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms	(sqrt PI)

series103.0ms

Counts

4 → 10

Calls

4 calls:

57.0ms	(* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms	(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms	(sqrt PI)

simplify59.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1376	4481
1	5001	2465

prune996.0ms

Filtered

342 candidates to 135 candidates (39.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	341	1	342
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	341	13	354

Merged error: 0.1b

Counts

354 → 13

regimes193.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	49
1	54	49
2	54	49

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.7s

22641×

body

valid